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%I #6 Jul 31 2021 21:57:16
%S 2676,2851,2916,4131,4226,4241,4306,4371,4481,4850,5346,5411,5521,
%T 5586,5651,6561,6611,6756,6771,6801,6821,6836,6851,6931,7106,7235,
%U 7475,7491,7666,7841,7906,7971,8146,8211,8321,8386,8451,8531,8706,9011,9156,9171,9186
%N Numbers that are the sum of six fourth powers in exactly three ways.
%C Differs from A345560 at term 18 because 6626 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 9^4 = 2^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4 = 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4.
%H Sean A. Irvine, <a href="/A345815/b345815.txt">Table of n, a(n) for n = 1..10000</a>
%e 2851 is a term because 2851 = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4.
%o (Python)
%o from itertools import combinations_with_replacement as cwr
%o from collections import defaultdict
%o keep = defaultdict(lambda: 0)
%o power_terms = [x**4 for x in range(1, 1000)]
%o for pos in cwr(power_terms, 6):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v == 3])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A048931, A344244, A345560, A345814, A345816, A345825, A346358.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 26 2021
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